Average Error: 0.1 → 0.1
Time: 6.8s
Precision: 64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[\mathsf{fma}\left(-x, \mathsf{fma}\left(0.12, x, 0.253\right), 1\right)\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
\mathsf{fma}\left(-x, \mathsf{fma}\left(0.12, x, 0.253\right), 1\right)
double f(double x) {
        double r280 = 1.0;
        double r281 = x;
        double r282 = 0.253;
        double r283 = 0.12;
        double r284 = r281 * r283;
        double r285 = r282 + r284;
        double r286 = r281 * r285;
        double r287 = r280 - r286;
        return r287;
}
↓
double f(double x) {
        double r288 = x;
        double r289 = -r288;
        double r290 = 0.12;
        double r291 = 0.253;
        double r292 = fma(r290, r288, r291);
        double r293 = 1.0;
        double r294 = fma(r289, r292, r293);
        return r294;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.1

    \[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(-x, \mathsf{fma}\left(0.12, x, 0.253\right), 1\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(-x, \mathsf{fma}\left(0.12, x, 0.253\right), 1\right)\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))